模糊完备格上的模糊同余关系-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

模糊完备格上的模糊同余关系

刘敏，赵彬*

（陕西师范大学数学与信息科学学院，陕西西安 710062）

刘敏,男,博士研究生,研究方向为格上拓扑学. E-mail: liumin2010@stu.snnu.edu.cn.*通信作者：赵彬,男,教授,博士研究生导师. E-mail: zhaobin@snnu.edu.cn.

摘要:

在模糊完备格中引入模糊完备格同余关系的概念，讨论了模糊完备格同余与模糊闭包算子之间的关系.证明了一个模糊完备格上的模糊同余关系之集构成的模糊偏序集模糊序同构于其上的模糊闭包算子之集构成的模糊偏序集.给出了模糊完备格同余的商的概念，证明了任一模糊完备格满同态的像都模糊序同构于由该模糊完备格同态所诱导的同余关系的商.

关键词：

模糊偏序集; 模糊完备格; 模糊完备格同余; 模糊闭包算子

收稿日期：

2012-07-05

中图分类号：

O159

文献标识码：

文章编号：

1672-4291(2013)01-0005-05

基金项目：

国家自然科学基金资助项目(11171196, 10871121).

Doi:

Fuzzy congruence relations on fuzzy complete lattices

LIU Min, ZHAO Bin*

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

The concept of fuzzy complete lattice congruence relation on fuzzy complete lattice is defined, and the relation between fuzzy complete lattice congruence and fuzzy closure operator is discussed. It is proved that in a fuzzy complete lattice, the fuzzy poset of fuzzy complete lattice congruence relations is fuzzy order isomorphic to the fuzzy poset of fuzzy closure operators. The quotient of a fuzzy complete lattice congruence relation is defined. It is also proved that the image of a fuzzy complete lattice under a surjective fuzzy complete lattice morphism is fuzzy order isomorphic to the quotient of the fuzzy complete lattice congruence relation induced by the fuzzy complete lattice morphism.

KeyWords:

fuzzy poset; fuzzy complete lattice; fuzzy complete lattice congruence relation; fuzzy closure operator